Consider `f(x)=sin3x,0<=x<=(pi)/(2),` then (a) `f(x)`is increasing for`x in(0,(pi)/(6))`and decreasing for `x in((pi)/(6),(pi)/(2))`(b) `f(x) is increasing forx in(0,(pi)/(4))` and decreasing for `x in((pi)/(4),(pi)/(2))` (c) `f(x)

Consider f(x)=[[2(sinx-sin^3x)+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx-sin^3x|]], x != pi/2 for x in (0,pi), f(pi/2) = 3 where [ ] denotes the greatest integer function then,

Consider f (x)= sin ^(5) x-1, x in [0, (pi)/(2)], which of the following is/are correct ?

Consider f, g and h be three real valued function defined on R. Let f(x)=sin3x+cosx,g(x)=cos3x+sinx and h(x)=f^(2)(x)+g^(2)(x). Then, The length of a longest interval in which the function g=h(x) is increasing, is

Consider f, g and h be three real valued function defined on R. Let f(x)=sin3x+cosx,g(x)=cos3x+sinx and h(x)=f^(2)(x)+g^(2)(x). h(x) = 4

Consider f, g and h be three real valued function defined on R. Let f(x)=sin3x+cosx,g(x)=cos3x+sinx and h(x)=f^(2)(x)+g^(2)(x). Then, The length of a longest interval in which the function h(x) is increasing, is

Find k if the function f(x)={(sin3x)/x ,x!=0;k/2,x=0 is continuous at x=0 . (a)3 (b) 6 (d) 9 (d) 12

The function f(x)={((sin3x)/x ,x!=0),(k/2,x=0):} is continuous of x=0,t h e nk= (a) 3 (b) 6 (d) 9 (d) 12

The function f(x)={(sin3x)/x ,x!=0k/2,x=0 is continuous of x=0,t h e nk= 3 (b) 6 (d) 9 (d) 12

Consider f(x) = {{:((8^(x) - 4^(x) - 2^(x) + 1)/(x^(2))",",x gt 0),(e^(x)sin x + pi x + k log 4",",x lt 0):} Then, f(0) so that f(x) is continuous at x = 0, is

Consider f, g and h be three real valued function defined on R. Let f(x)=sin3x+cosx,g(x)=cos3x+sinx and h(x)=f^(2)(x)+g^(2)(x). Then, Number of point (s) where the graphs of the two function, y=f(x) and y=g(x) intersects in [0,pi] , is